Spatial Differentiation of Climate Risks Across U.S. Metropolitan Statistical Areas: An Empirical Analysis Based on PCA and K-Means Clustering

In the context of intensifying climate change, understanding the spatial heterogeneity of urban climate risk is critical to effective climate governance in the United States. This study takes 251 major Metropolitan Statistical Areas (MSAs) in the United States as the analytical unit and establishes a multidimensional urban climate risk assessment framework covering hazard risk, exposure vulnerability, and adaptive capacity. Principal Component Analysis (PCA) is adopted for dimensionality reduction to extract key factors, and K-means clustering is used to identify the spatial differentiation characteristics of climate risk across these MSAs. The results show that climate risk in U.S. MSAs presents significant spatial disparities and can be categorized into four types: high resource and adaptive capacity, high exposure with insufficient adaptive support, complex socio-environmental vulnerability, and low current vulnerability with latent cumulative risk. Based on these findings, this study proposes targeted policy recommendations, including promoting inter-MSA coordination and adaptive capacity spillover, implementing gray–green integrated infrastructure development and enhancing social resilience in the southeastern coastal regions, strengthening equity orientation in climate governance, and advancing proactive governance of cumulative and chronic risks. These conclusions provide a reference for relevant authorities to formulate climate policies.